2. $\quad+-150$ points Devorestat9 4.E.011. Let $X$ denote the amount of time a book on two-hour reserve is actually checked out, and suppose the caf is the following. $$ F(x)=\left\{\begin{array}{11} O & x3.5)$. (d) What is the median checkout duration $\tilde{\mu} $ ? solve $0.5=F(\tilde{\mu})]$. (e) Obtain the density function $f(x) $. $f(x)=F^{\prime} (x)=$ (f) Calculate $E(X)$. (g) Calculate $v(x)$ and $\sigma_{x}$ - $v(x)=$ $\sigma_{x}=$ (h) If the borrower is charged an amount $h(x)=x^{2}$ when checkout duration is $x$, compute the expected charge $\varepsilon[h(x)]$. SP.AS403